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Influence of the Cage Size on the Dynamic Behavior of Fullerenes: A Study of 13C NMR SpinⴚLattice Relaxation Sabrina Klod and Lothar Dunsch* Department of Electrochemistry and Conducting Polymers, IFW Dresden, Helmoltzstr. 20, D-01069 Dresden, Germany
ABSTRACT A detailed study on the relaxation mechanisms of higher cage fullerene sizes is done as a prerequisite for studies of the influence of the endohedral structures on fullerene cage carbon relaxation. Recent studies of the dynamic behavior of C60 and C70 in aromatic solvents and CS2 solution show the influence of the shape and the symmetry of the cage to be highly important as well as the influence of the solvent to be negligible. As higher fullerene cages have more than one stable isomer, the isolation of isomeric pure structures is of high importance for a detailed study of the dynamic behavior of such fullerenes. Here we investigated the three higher fullerene cage isomers D2-C76, C2v(3)-C78, and D2-C80 with respect to the relaxation rate of the carbons measured in their temperature dependence. Thus, we study the influence on the relaxation of the carbons and the dynamic behavior of these fullerenes in solution. Besides the diffusion dependence on the shape of the carbon cage, the relaxation behavior at lower temperatures is found to be dependent on the difference in chemical shift anisotropy within the carbon cage. This difference is originated from the changes of symmetry and results in polarization of electron density. Furthermore, the mobility of the carbons is influenced by their pyramidalization. KEYWORDS: fullerenes · 13C NMR spectroscopy · carbon relaxation · symmetry · C76 · C78 · C80
uclear magnetic resonance relaxation measurements as a powerful tool to investigate molecular motion in solution were used in different NMR studies.1⫺5 It has been shown that 13C relaxation in fullerenes is very slow due to the absence of protons at the carbon atoms of the fullerene cage. Chemical shift anisotropy (R1CSA) and spin rotation (R1SR) solely participate in the 13C relaxation of fullerenes. A separation of these two contributions is realized by the field strength dependence of the R1CSA mechanism and the R1SR mechanism via its temperature dependence.6,7 If a measurement of the relaxation behavior for different field strengths is impossible, the separation of the relaxation mechanism contributions via the Hubbard relation gives reliable results.8 Therefore, the temperature region with small step diffusion has to be localized in the temperature dependence of the relaxation rate. Here, the chemical shift anisot-
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*Address correspondence to
[email protected]. Received for review February 1, 2010 and accepted May 5, 2010. Published online May 11, 2010. 10.1021/nn1002024 © 2010 American Chemical Society
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ropy part of the relaxation is dominant, and an easy separation of the two relaxation mechanisms is possible via the Hubbard relation. The thus-separated contributions to the experimental relaxation rate are used to study the molecular motion in solution. The reorientational rotation is studied via the chemical shift anisotropy contribution in the temperature range of small step diffusion. The analysis of the spin rotation contribution leads to conclusions on the diffusion behavior of the molecule.4 To understand the role of the cluster in endohedral nitride cluster fullerenes,9 several larger fullerene cages were to be studied. Among the endohedral cluster fullerenes, the highest stability is found for the Ih-C80 and D5h-C80 cage isomers, but other cage sizes of cluster fullerenes are stabilized, as well.10,11 In the arc burning process for fullerene formation, C60 and C70 are the most stable cages and are available in larger amounts. Furthermore, these fullerenes exist in only one stable cage isomer. Relaxation measurements of these molecules in CS2 solution lead to the conclusion that the shape of the fullerene cage is essential for the relaxation and, therefore, for the rotation as well as diffusion of these fullerene molecules. The two different rotation axes in C70 were shown to have different rotation energies. The role of the solvent is due to different solvation shells and to the hindrance of motion in solution.5 The aim of this work is a detailed study of the relaxation mechanisms of fullerenes with higher cage sizes as a prerequisite for studies on the role of the endohedral nitride clusters in fullerene cage relaxation. As the fullerene cages consist of pentagons and hexagons, the carbon atoms can be divided www.acsnano.org
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Figure 1. D2-C76 molecule symmetry and its 13C NMR spectrum.
Scheme 1. Pyrene carbons (a) and corannulene carbons (b) in fullerenes.
into two different types. Pyrene-like carbons are situated at linked hexagons, whereas corannulene-like carbons are those in the center of two hexagons and one pentagon (see Scheme 1). To extend the family of fullerenes, the possible cage sizes C72, C74, C76, C78, and C80 have to be considered with regard to additional parameters in 13C relaxation. While C72 and C74 are not stable to be isolated as an empty fullerene structure,12 other cages offer at least one stable isomer which can be isolated in an isomeric pure form in reasonable amounts. One isomer of every of these fullerenes was isolated by a multistep HPLC separation of a fullerene soot produced by arc synthesis.13 These isomers were used to study the relaxation rate of the different carbons in their temperature dependence to extend our knowledge on the influence of the cage size, symmetry, and shape on the dynamic behavior of these fullerenes in solution.
Figure 2. Correlation of the relaxation rate R1 and the chemical shift of the 19 different carbon signals of D2-C76 at 268 and 298 K.
dence of the relaxation rates in a range from 268 to 298 K (Figure 3) gives a similar behavior for all 19 different cage carbons. Like for D5h-C70, the relaxation rate decreases with increasing temperature in the whole temperature range. Generally, the temperature dependence of the relaxation rate shows the very slow diffusion contribution as compared to the rotation of the molecule in the time scale of NMR. The values of the relaxation rate for the whole molecule are larger than
RESULTS AND DISCUSSION Here we study C76 as the D2 isomer and C78 as the C2v(3) isomer, while the main C80 cage isomer has a D2 symmetry. To start with the lowest cage size in the row, the D2 isomer of C76 is investigated. The 13C NMR spectrum (Figure 1) has 19 different carbon signals, as expected for the symmetry of the molecule. The shape of the molecule (Figure 1) is rather similar to the D5hC70 cage. The relaxation rates were measured in dependence on the chemical shift of the 19 independent carbon signals for two different temperatures (Figure 2). At 268 K, a correlation of the relaxation rate and the chemical shift is observed. At higher chemical shifts, the relaxation rate increases. At 298 K, the relaxation rate values are more scattered and the correlation to the chemical shift is lower. The temperature depenwww.acsnano.org
Figure 3. Temperature dependence of the relaxation rate R1 of D2C76. VOL. 4 ▪ NO. 6 ▪ 3236–3240 ▪ 2010
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ARTICLE Figure 4. C2v(3)-C78 molecule symmetry and its 13C NMR spectrum.
Figure 5. Correlation between relaxation rate R1 and chemical shift of the 22 different carbon signals of C2v(3)-C78 at 268 and 298 K.
in C70, which can be attributed to the lower symmetry of the C76 molecule. The pyrene carbons of D2-C76 have a shift to higher field in the same chemical shift range like the pyrene carbon C-5 of C70, which might be the consequence of the low pyramidality of the carbons.14,15 These carbons show a similar relaxation behavior. The corannulene carbons of the C76 molecule
Figure 6. Temperature dependence of the relaxation rate R1 of C2v(3)-C78.
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can be found at lower fields as a consequence of a higher pyramidality.15 In comparison to the pyrene carbons, the corannulene carbons show higher relaxation rates like the corannulene carbons C-1 to C-4 in C70. The similar shape of the molecules leads to a similar distribution of relaxation rates. The lower symmetry of the C76 molecule is the reason for a higher anisotropy in electron density distribution and higher relaxation rates in this molecule. The isolated C2v(3) isomer of C78 has a more spherical shape (Figure 4) than the D2 isomer of C76 and is more comparable to Ih-C60. The 13C NMR spectrum (Figure 4) of C2v(3)-C78 consists of 22 lines with 17 lines of double intensity and 5 lines of half intensity as expected from the symmetry of the molecule. The relaxation rates dependent on the chemical shift of the 22 different carbon signals were measured for two different temperatures (Figure 5). With higher chemical shifts of the different carbons, the relaxation rates increase although the slope is more flat as compared to D2-C76. The chemical shift range and relaxation rates are smaller compared to D2-C76. The pyrene and corannulene carbons do not differ in chemical shift or relaxation rate. The temperature dependence of the relaxation rates (Figure 6) shows the same behavior as the other fullerene cages: the relaxation rates decrease with increasing temperature. Also in this case, the rotation is fast compared to the diffusion of the molecule, but the relaxation rates of the C2v(3) isomer of C78 at 268 K are lower than that for D2-C76, while at 298 K, they are higher than for the D2 isomer of C76 but smaller than for C60. Therefore, a stronger influence of the diffusion on the overall relaxation rate but a smaller influence of electron density shifts can be concluded for this molecule with a higher curvature. Although the isolated amount of the D2 isomer of C80 was smaller compared to the other cages, the 13 C NMR spectrum shows a sufficient signal-to-noise ratio (Figure 7). The 19 lines among which one is of higher intensity point to the 20 independent carbons in the cage where 2 lines overlap. The concentration in solution was too low for a detailed temperature-dependent www.acsnano.org
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Figure 7. D2-C80 molecule symmetry and its 13C NMR spectrum.
analysis of the relaxation behavior. Only the relaxation rate at 298 K could be measured in a reasonable experimental time scale. The relaxation rate of the 19 carbon signals in relation to their chemical shift (Figure 8) gives no clear correlation between chemical shift and relaxation rate, although a trend similar to that in D2-C76 is observable. The relaxation rates are slightly increased as compared to D2-C76 at the same temperature. Here a small cage size effect on the relaxation behavior can be seen. In this larger fullerene cage, the electron density distribution of the molecule is more polar and, therefore, the anisotropy in the molecule is stronger. In summary, the relaxation rate of fullerenes with larger cage sizes is higher than for smaller cage sizes of C60 and C70. The shape of the molecule has an influence on the diffusion rate of the fullerene. The difference in rotation of the molecules is also determined by the shape for the two different rotation axes in C70.5 The relaxation behavior at lower temperatures shows a difference in anisotropy of the chemical shift within the carbon cage. A polarization of the electron density in the molecule originates from the different symmetry and can result in a different shielding of the carbon nuclei by electrons. Therefore, the chemical shifts as well as the relaxation rates are influenced by a higher shielding effect of the electron density and are correlated with each other. While in molecules with larger curvature such as C2v(3)-C78 the relaxation rates are rather similar, larger deviations in relaxation rates are observed for the different kinds of carbons in eggshaped molecules like D5d-C70 and D2-C76. Investigating chemical shifts and relaxation rates in a positively charged fullerene should result in an increase in relaxation rate and chemical shift by a reduced electron density in the molecule, but the cations of these fullerenes are difficult to produce in solution because of their high oxidation potentials. The relaxation rate of the carbons is also correlated to their pyramidality. As the relaxation rate is a matter of mobility of atoms in the molecular backbone, the higher pyramidal carbons show higher vibrating mobility. This effect might increase their relaxation rate. The www.acsnano.org
differences of the relaxation rates of carbons at the top of an egg-shaped molecule compared to that at the side can also result from the different rotation around the two rotation axes, which is not obtained for spherical molecules.5 Furthermore, the cage size effect for the same cage symmetry has a similar influence on the anisotropy in the molecule, and therefore, the relaxation is increased. Here, the comparison with larger cages such as C84 for different isomers should give additional insights into the relaxation behavior. The analysis of the role of the cluster in the relaxation of endohedral nitride cluster fullerenes and other endohedral fullerenes can be based on these results. The most stable endohedral nitride cluster fullerenes are the family of C80 cage size, where mainly the Ih and in lower amount the D5h isomer are formed. Unfortunately, these cages are among the most unstable C80 cage isomers within the family of empty fullerenes, and the isolation in larger amounts for a detailed 13C NMR study is not possible.12 As to the analysis of endohedral nitride cluster fullerenes of the Ih-C80 cage isomers, the higher symmetry as well as the spherical shape of the
Figure 8. Relaxation rate R1 versus chemical shift of the 19 different carbon signals of D2-C80 at 298 K. VOL. 4 ▪ NO. 6 ▪ 3236–3240 ▪ 2010
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molecule leads to a similar electron density distribution and should result in a dynamic behavior of the Ih-C80 carbon cage similar to Ih-C60. CONCLUSION To extend the family of empty fullerenes, we investigated the three higher fullerenes D2-C76, C2v(3)-C78, and D2-C80. The isomeric pure fullerene structures were isolated by recycling HPLC from a fullerene soot produced by arc discharge synthesis. The influence of different parameters such as cage size, symmetry, and shape on the 13C relaxation rate
METHODS Fullerenes under study were obtained from a Kra¨tschmer⫺ Huffmann arc synthesis of graphite rods.10,11,14 The soot from the arc discharge synthesis was washed with acetone and extracted by Soxhlet extraction with CS2 for 20 h. The extract was dried and redissolved in toluene for HPLC separation. The fullerenes were isolated by multistage HPLC separation with toluene as solvent.13 In a final step, the isolated fullerene was dried and washed with acetone and n-hexane to remove toluene and PAHs and redissolved in CS2. NMR measurements were performed on a Bruker Avance II 500 (Bruker Biospin) at a magnetic field strength of 11.74 T. Relaxation times were obtained using the standard inversion recovery pulse sequence (D1--D2-/2) with waltz-decoupling sequence for proton decoupling and relaxation durations (D1) of 5 times the expected T1 and with a variation of D2 from 1 to 50 s. Samples were prepared in a 5 mm tube under nitrogen atmosphere to avoid any oxygen influence on T1 measurements. As an external lock, acetone-d6 and DMSO-d6 in a coaxial tube were used. The spectra were calibrated using the signal of the lock solvent. Temperature control via a heating and cooling unit BC-U 05 (Bruker Biospin) leads to a temperature accuracy of 0.1 K. The signal intensities in dependence on the D2 time are observed showing an exponential decay. From the exponential fit of intensities versus D2, the relaxation rates R1 were extracted and relaxation times T1 calculated. The obtained relaxation rates are given as the sum of the different contributions to the relaxation mechanism. In the case of fullerene molecules, only the chemical shift anisotropy and spin rotation contribute to the relaxation rate (eq 1):6
R1 ) 1/T1 ) R1CSA + R1SR
(1)
in these fullerenes was studied. While the shape of the fullerene molecule has an influence on the diffusion rate, the difference in rotation of the molecules is negligible. The relaxation behavior at lower temperatures is dependent on the cage symmetry, causing a difference in anisotropy of the chemical shift at the carbon cage by polarization of the electron distribution. The cage size effect at the same symmetry is caused by a higher polarization of the electron density, resulting in an additional influence on the anisotropy of the molecule and an influence on the relaxation.
6. Becker, E. D. High Resolution NMR: Theory and Applications; Academic Press: New York, 1980. 7. Abragam, A. The Principles of Nuclear Magnetism; Oxford University Press: New York, 1961. 8. Hubbard, P. S. Theory of Nuclear Magnetic Relaxation by Spin-Rotational Interactions in Liquids. Phys. Rev. 1963, 1155–1165. 9. Klod, S.; Zhang, L.; Dunsch, L. The Role of the Cluster on the Relaxation of Endohedral Fullerene Cage Carbons: A NMR Spin-Lattice Relaxation Study of an Internal Relaxation Reagent. J. Phys. Chem. C. 2010, 8264–8267. 10. Dunsch, L.; Yang, S. Endohedral ClusterfullerenesOPlaying with Cluster and Cage Sizes. Phys. Chem. Chem. Phys. 2007, 3067–3081. 11. Dunsch, L.; Yang, S. Metal Nitride Cluster Fullerenes: Their Current State and Future Prospects. Small 2007, 1298–1320. 12. Taylor, R. The Chemistry of Fullerenes; World Scientific: Singapore, 1995. 13. For details, see: Zalibera, M.; Rapta, P.; Popov, A. A.; Dunsch, L. Charged States of Four Isomers of C-84 Fullerene: In Situ ESR and Vis⫺NIR Spectroelectrochemistry and DFT Calculations. J. Phys. Chem. C 2009, 5141–5149. 14. See the recent study: Yang, S. F.; Popov, A. A.; Dunsch, L. The Role of an Asymmetric Nitride Cluster on a Fullerene Cage: The Non-IPR Endohedral DySC2N@C-76. J. Phys. Chem. B 2007, 13659–13663. 15. (a) Heine, T.; Bu¨hl, M.; Fowler, P. W.; Seifert, G. Modelling the C-13 NMR Chemical Shifts of C-84 Fullerenes. Chem. Phys. Lett. 2000, 373–380. (b) Sun, G. Y.; Kertesz, M. Isomer Identification for Fullerene C-84 by C-13 NMR Spectrum: A Density-Functional Theory Study. J. Phys. Chem. A 2001, 5212–5220.
Acknowledgment. We thank Kristina Leger for the isolation of the fullerene structures, and Sandra Schiemenz and Marco Senf (all of IFW Dresden) for technical assistance.
REFERENCES AND NOTES 1. Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Science of Fullerenes and Carbon Nanostructures; Academic Press: San Diego, CA, 1996. 2. Canet, D.; Robert, J. B.; Tekely, P. C-13 NMR RelaxationTime of Fullerene as a Function of Magnetic-Field. Chem. Phys. Lett. 1993, 483–486. 3. Shang, X.; Fisher, L. A.; Rodriguez, A. A. C-13 Spin⫺Lattice Relaxation and Molecular Dynamics of C-60 in 1,2Dichlorobenzene-d4. J. Phys. Chem. 1996, 4361–4364. 4. Shang, X.; Rodriguez, A. A. Anomalous Relaxation and Molecular Dynamics of Buckminsterfullerene in Carbon Disulfide. J. Phys. Chem. A 1997, 103–106. 5. Klod, S.; Dunsch, L. The Role of Aprotic Solvents in the Dynamic Behavior of Fullerenes like C-60 and C-70: A NMR Spin⫺Lattice Relaxation Study. J. Phys. Chem. C 2009, 15191–12195.
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